Nonlinear higher-order shell theory for incompressible biological hyperelastic materials

In the present study, a geometrically nonlinear theory for circular cylindrical shells made of incompressible hyperelastic materials is developed. The 9-parameter theory is higher-order in both shear and thickness deformations. In particular, the four parameters describing the thickness deformation are obtained directly from the incompressibility condition. The hyperelastic law selected is a state-of-the-art material model in biomechanics of soft tissues and takes into account the dispersion of collagen fiber directions. Special cases, obtained from this hyperelastic law setting to zero one or some material coefficients, are the Neo-Hookean material and a soft biological material with two families of collagen fibers perfectly aligned. The proposed model is validated through comparison with the exact solution for axisymmetric cylindrical deformation of a thick cylinder. In particular, the shell theory developed herein is capable to describe, with extreme accuracy, even the post-stability problem of a pre-stretched and inflated Neo-Hookean cylinder until the thickness vanishes. Comparison to the solution of higher-order shear deformation theory, which neglects the thickness deformation and recovers the normal strain from the incompressibility condition, is also presented. (C) 2018 Elsevier B.V. All rights reserved.